Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y

Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y >

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 02 Jan 2008

Posts: 196

Location: Toronto

Followers: 1

Kudos [?]: 27 [0], given: 0

Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y > [#permalink]

20 Mar 2008, 10:19

00:00

Question Stats:

0% (00:00) correct

0% (00:00) wrong

based on 1 sessions

Is x^4 + y^4 > z^4

(1) X^2 + y^2 > z^2
(2) X + Y > Z

CEO

Joined: 29 Aug 2007

Posts: 2530

Followers: 41

Kudos [?]: 358 [0], given: 19

Re: DS : Is x4 + y4 > z4 [#permalink]

20 Mar 2008, 10:35

maverick101 wrote:

Is x^4 + y^4 > z^4

(1) X^2 + y^2 > z^2
(2) X + Y > Z

E.

1 & 2:
if x = y = 0.8 and z = 0.9 ---- yes.
if x = y = 0.7 and z = 0.9 ------- no.
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

CEO

Joined: 17 Nov 2007

Posts: 3596

Concentration: Entrepreneurship, Other

Schools: Chicago (Booth) - Class of 2011

GMAT 1: 750 Q50 V40

Followers: 231

Kudos [?]: 1300 [0], given: 346

Re: DS : Is x4 + y4 > z4 [#permalink]

20 Mar 2008, 10:38

E

Is x^4 + y^4 > z^4

(1) x^2 + y^2 > z^2

(2) x + y > z

It is obviously that x=10000, y=10000, z=1 satisfies both conditions and answer is "true".
So, I will try to construct example that satisfies both condition but answer is "false"
1. let x=y and z=1 for simplicity.
2. we need x<1 because x^n will decrease when the power increases.
consider the fist condition: 2*x^2>1 --> x>\sqrt{0.5} \approx 0.7
3. try x=0.8 (it satisfies both conditions): 2*0.8^4 = 2*0.64^2 < 2*0.7^2 < 2*0.49 < 1 bingo!

Here, I've tried to clarify my logic (for myself also

) when I construct examples.....just exercise :shock:

_________________

iOS/Android: GMAT ToolKit - The bestselling GMAT prep app | GMAT Club (free) | PrepGame | GRE ToolKit | LSAT ToolKit
PROMO: Are you an exiting GMAT ToolKit (iOS) user? Get GMAT ToolKit 2 (iOS) for only $0.99 (read more)
Math: GMAT Math Book ||| General: GMATTimer ||| Chicago Booth: Slide Presentation
The People Who Are Crazy Enough to Think They Can Change the World, Are the Ones Who Do.

Re: DS : Is x4 + y4 > z4 [#permalink] 20 Mar 2008, 10:38

	Similar topics	Author	Replies	Last post
Similar Topics:	is x^4 + y^4 > z^4? 1. x^2 + y^2 > z^2 2. x+y > z	Jennif102	5	06 Nov 2005, 21:52
	Is X^4 + Y^4 > Z^4? (1) X^2 + Y^2 > Z^2 (2) X + Y >	ffgmat	15	17 Dec 2005, 10:46
	Is x^4 + y^4 > z^4? 1) x^2 + y^2 >z^2 2) x +y >z	jjhko	7	02 Sep 2006, 18:46
	Is x^4 + y^4 > z^4 (1) x^2 + y^2 > z^2 (2) x + y >	kidderek	3	23 Nov 2006, 15:18
	Is x^4 + y^4 > z^4 1. x^2 + y^2 > z^2 2. x + y > z	study	2	19 Nov 2008, 03:29

Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y >

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y >

Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y >

Main navigation

GMAT Resources

Partners

MBA Resources